Abstract: The superharmonic and subharmonic resonance responses of a strongly nonlinear delay differential equation are solved using an incremental harmonic balance method. The value of the exciting frequency when the subharmonic resonance occurs is discussed. The influences of the time delay, the feedback gain, the excitation amplitude and the coefficient of nonlinear terms on the system superharmonic and subharmonic resonance response are studied. The results show that the influences of each system parameter on the superharmonic resonance response and the subharmonic resonance response of the system are great. The value of the exciting frequency when the subharmonic resonance occurs is affected by the system parameters.